Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed

被引：14

作者：

Moisio, Marko ^{[2
]}

Ranto, Kalle ^{[1
]}

机构：

[1] Univ Turku, Dept Math, FIN-20014 Turku, Finland

[2] Univ Vaasa, Dept Math & Stat, FIN-65101 Vaasa, Finland

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2008年 / 14卷 / 03期

基金：

芬兰科学院;

关键词：

Kloosterman sum; exponential sum function field; rational place; Dickson polynomial; BCH coded; Melas code;

D O I：

10.1016/j.ffa.2008.01.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F-q be a finite field of characteristic p = 2, 3. We give the number of irreducible polynomials x(m) + a(m-1) x(m-1) + ... + a(0) F-q [x] with a(m-1) and a(m-3) prescribed for any given in if p = 2, and with a(m-1) and a(1) prescribed for m = 1,.... 10 if p = 2, 3. In the latter case an enumeration formula, applicable also if m > 10, is given, but it is explicit only up to the evaluation of certain Kronecker class numbers. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：798 / 815

页数：18

共 16 条

[1] [Anonymous], 1997, ENCY MATH APPL
[2] EXPLICIT EVALUATION OF CERTAIN EXPONENTIAL SUMS
CARLITZ, L
[J]. MATHEMATICA SCANDINAVICA, 1979, 44 (01) : 5 - 16
[3] Primitive elements with zero traces
Chou, WS
Cohen, SD
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2001, 7 (01) : 125 - 141
[4] Kloosterman sums and primitive elements in Galois fields
Cohen, SD
[J]. ACTA ARITHMETICA, 2000, 94 (02) : 173 - 201
[5] Explicit theorems on generator polynomials
Cohen, SD
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2005, 11 (03) : 337 - 357
[6] Irreducible polynomials over GF(2) with three prescribed coefficients
Fitzgerald, RW
Yucas, JL
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2003, 9 (03) : 286 - 299
[7] ELEMENTARY ABELIAN P-EXTENSIONS OF ALGEBRAIC FUNCTION-FIELDS
GARCIA, A
STICHTENOTH, H
[J]. MANUSCRIPTA MATHEMATICA, 1991, 72 (01) : 67 - 79
[8] Lidl R., 1993, PITMAN MONOGR SURV P, V65
[9] MOISIO M, 2008, FINITE FIEL IN PRESS
[10] The moments of a Kloosterman sum and the weight distribution of a Zetterberg-type binary cyclic code
Moisio, Marko J.
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (02) : 843 - 847

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